Question

A bus is moving with a speed of $ 10 \,ms^{-1} $ on a straight road. A scooterist wishes to overtake the bus in $ 100 \,s $ . If the bus is at a distance of $ 1 \,km $ from the scooterist with what speed should the scooterist chase the bus ?

• A. $ 40 \,ms^{-1} $
• B. $ 25 \,ms^{-1} $
• C. $ 10 \,ms^{-1} $
• D. $ 20 \,ms^{-1} $

Answer 1

The Correct Option is D

To determine the speed at which the scooterist should travel to overtake the bus in 100 seconds, we start by considering the given parameters:

• The speed of the bus is $10 \, \text{ms}^{-1}$.
• The scooterist has a time limit of $100 \, \text{s}$ to overtake the bus.
• The initial distance between the scooterist and the bus is $1 \, \text{km} = 1000 \, \text{m}$.

Let's denote the required speed of the scooterist as $v \, \text{ms}^{-1}$.

The scooterist needs to cover the initial distance of $1000 \, \text{m}$ plus the distance the bus travels in 100 seconds to overtake it. The distance the bus travels in this time can be calculated as follows:

Distance_{\text{bus}} = \text{Speed}_{\text{bus}} \times \text{Time} = 10 \, \text{ms}^{-1} \times 100 \, \text{s} = 1000 \, \text{m}

Therefore, the total distance the scooterist needs to cover is:

Total \, Distance_{\text{scooterist}} = 1000 \, \text{m} + 1000 \, \text{m} = 2000 \, \text{m}

To cover this distance in 100 seconds, the speed of the scooterist must be:

v = \frac{\text{Total \, Distance}_{\text{scooterist}}}{\text{Time}} = \frac{2000 \, \text{m}}{100 \, \text{s}} = 20 \, \text{ms}^{-1}

Therefore, the correct answer is that the scooterist should travel at a speed of $20 \, \text{ms}^{-1}$ to overtake the bus in 100 seconds.